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[[Stirling numbers of the second kind]] may be derived and analyzed using the structural decomposition
:<math> \mathfrak{P}(\mathfrak{P}_{\ge 1}(\mathcal{Z})).</math>
The decomposition
:<math> \mathfrak{P}(\mathfrak{C}(\mathcal{Z}))</math>
is used to study unsigned [[Stirling numbers of the first kind]], and in the derivation of
the [[Random permutation statistics|statistics of random permutations]].
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